# Properties

 Label 1805.654 Modulus $1805$ Conductor $95$ Order $6$ Real no Primitive no Minimal no Parity odd

# Related objects

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(6))

M = H._module

chi = DirichletCharacter(H, M([3,1]))

pari: [g,chi] = znchar(Mod(654,1805))

## Basic properties

 Modulus: $$1805$$ Conductor: $$95$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$6$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{95}(84,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1805.h

sage: chi.galois_orbit()

order = charorder(g,chi)

[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Related number fields

 Field of values: $$\mathbb{Q}(\zeta_3)$$ Fixed field: 6.0.309512375.1

## Values on generators

$$(362,1446)$$ → $$(-1,e\left(\frac{1}{6}\right))$$

## First values

 $$a$$ $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$11$$ $$12$$ $$13$$ $$\chi_{ 1805 }(654, a)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 1805 }(654,a) \;$$ at $$\;a =$$ e.g. 2